Visualization-Assisted Teaching Reform of the Mathematical Analysis Course for Information and Computing Science Majors in Local Applied Universities

Abstract

: Mathematical Analysis is a core foundational course for Information and Computing Science majors, but its high level of abstraction, rigorous logical structure, and emphasis on symbolic reasoning often make it difficult for students in local applied universities. Traditional teaching usually focuses on definitions, theorem proofs, and computational exercises, while students’ geometric intuition, computational thinking, and awareness of applications are not sufficiently developed. To address these problems, this paper explores a visualization-assisted teaching reform of the Mathematical Analysis course for Information and Computing Science majors in local applied universities. A teaching framework is proposed by integrating symbolic expression, geometric visualization, numerical experiment, and application interpretation. Within this framework, four dimensions are discussed: concept visualization, process visualization, relation visualization, and application visualization. Typical teaching examples, including limits, derivatives, definite integrals, series convergence, and gradients, are used to illustrate how visualization tools can support students’ understanding of abstract concepts and help them connect mathematical theory with computational applications. The proposed approach emphasizes that visualization should not replace rigorous mathematical reasoning, but should serve as a bridge between intuition and proof, theory and computation, and mathematics and application. This study provides a practical reference for improving the teaching quality of Mathematical Analysis and cultivating applied, computational, and innovative talents in Information and Computing Science majors.